Liquid dispenser systems, such as liquid soap and sanitizer dispensers, provide a user with an amount of liquid upon actuation of the dispenser. It is desirable to provide such a dispenser having a rigid container that is vented with air so that the pump may re-prime itself after a dispensing action. It is also desirable to provide such a dispenser that is easily recharged once the container runs out of liquid to dispense, and that is inexpensive to produce. Many prior art venting systems for containers leak when placed in an inverted position wherein the container of liquid is located above the pump. In addition, many prior art venting systems also leak when they are intermittently exposed to liquid. Further, over tightening of the pump to the container may cause the container to leak, or seal venting passages preventing the container from venting properly.